Millions of pounds will be saved by reducing the number of "quangos" and cutting the pay of senior staff in those public bodies that survive, David Cameron pledged today.

In an echo of pledges made by Tony Blair in opposition – and by Margaret Thatcher in the 1980s – Cameron set out a three-point plan to overhaul organisations such as Britain's broadcasting regulator, Ofcom. But the Tory party leader's plan to trim the number of quangos (quasi autonomous non-government organisations) ran into trouble when Labour pointed out that the Tories planned to create 17 new quangos if they were elected to power.

The Conservatives rejected this figure, but admitted that their plans include the creation of what is expected to be the largest quango in British history, an independent board to run the NHS, and the most powerful – an office for budget responsibility to set Britain's fiscal framework.

The row broke out after Cameron said he would cut back on Britain's 790 quangos – 68 of which are led by executives earning more than Gordon Brown's £194,000 salary – that control £34bn. In a speech to the Reform thinktank, he said: "Too much of what government does is actually done by people that no one can vote out, by organisations that feel no pressure to answer for what happens, and in a way that is relatively unaccountable."

Quangos would have to meet at least one of three criteria to survive:

• Technical advice. The Bank of England's Monetary Policy Committee, which sets interest rates, and the National Institute for Clinical Excellence, which advises on which drugs the NHS can prescribe, would be retained in this category.

• Impartial decisions. Research councils, which allocate academic research grants free from government interference, would survive.

• Transparency. A fully independent Office for National Statistics, which gives important economic advice, would be retained. Under this category a new office for budget responsibility, to produce Britain's budget forecasts, would be established.

The quangos that survive would be trimmed as they carry out what Cameron described as "strictly administrative functions". Policy work carried out by quangos would be returned to Whitehall departments to ensure there was greater parliamentary accountability via ministers.

"There will be no more hiding behind the cloak of quango independence: ministers, not quangos, must answer for the outcomes of their policies," Cameron said. "Ministers must take responsibility for serious performance failures."

A major casualty would be Ofcom, Britain's broadcasting regulator. It would retain its technical functions, such as licensing the spectrum, but would lose its public policy role, such as deciding the future of regional news or Channel 4.

"With a Conservative government, Ofcom as we know it will cease to exist. Its remit will be restricted to its narrow technical and enforcement roles. It will no longer play a role in making policy."

Reducing the number of quangos would also cut costs. Cameron said after his speech that his cautious approach on public sector pay – he had earlier indicated that he had no plans to interfere with the independent bodies that set public sector pay, as he refused to endorse calls for a pay freeze – did not apply to quangos.

Labour believes Cameron's plans are inconsistent with his pledge to create an independent NHS board. Andy Burnham, the health secretary, said: "The Tories are planning to create the quango to end all quangos, which would control billions of pounds of public money without any direct ministerial oversight. That undermines their claim that they want to improve ministerial accountability."